Problem 64 - Elementary and Intermediate Algebra

Question

Lynn has \(\$ 350\) in her checking account. She writes a check for \(\$ 530,\) makes a deposit of \(\$ 75,\) and then writes a check for \(\$ 90 .\) What is the balance in her account?

Step-by-Step Solution

Answer

Lynn's account balance is \( -\$ 195 \).

Step 1: Initial Amount

Start with the initial amount in Lynn's checking account. Lynn has \( \$ 350 \) in her account.

Step 2: Subtract First Check

Subtract the amount of the first check from the initial amount. Lynn writes a check for \( \$ 530 \): \[ 350 - 530 = -180 \]

Step 3: Add the Deposit

Add the amount she deposited back to the account. Lynn makes a deposit of \( \$ 75 \): \[ -180 + 75 = -105 \]

Step 4: Subtract Second Check

Subtract the amount of the second check from the current balance. Lynn writes another check for \( \$ 90 \): \[ -105 - 90 = -195 \]

Step 5: Find the Final Balance

The final balance in Lynn's account is \( -195 \). This means Lynn's account is overdrawn by \( \$ 195 \).

Key Concepts

Account Overdrawn

When Lynn writes checks that exceed her checking account balance, her account becomes overdrawn. This means she has spent more money than she has in the account.

In this exercise, Lynn starts with a balance of \(350. She writes a check for \)530 which immediately takes her balance to -\(180, indicating she is overdrawn by \)180.

Even though she makes a deposit of \(75 afterwards, and writes another check for \)90, the account remains overdrawn.

At the end of all these transactions, her final balance is -\(195. This overdrawn status suggests she owes the bank \)195 since her account cannot cover the expenses.

Basic Arithmetic Operations

Understanding how to perform basic arithmetic operations like addition and subtraction is crucial for managing checking account balances.

1. **Subtraction**: When Lynn writes a check of \(530, you subtract this amount from her initial balance of \)350: \[ 350 - 530 = -180 \]
2. **Addition**: When she deposits \(75 into her account, you add this amount to the previous balance: \[ -180 + 75 = -105 \]
3. **Subtraction again**: Finally, when she writes another check for \)90, you subtract this amount from the current balance: \[ -105 - 90 = -195 \]

Each of these operations helps determine the updated balance at each stage. Learning these basic operations can significantly aid in tracking account balances effectively.

Step-by-Step Solution

Let’s walk through the solution steps one by one, fully understanding each stage:

1. **Initial Amount**: Start with the initial amount in Lynn's checking account, which is \(350. This is your starting point.

2. **Subtract First Check**: Subtract the first check amount (\)530) from the initial balance (\(350). The calculation is: \[ 350 - 530 = -180 \]
This means now her balance is -\)180.

3. **Add the Deposit**: Next, add the amount of the deposit (\(75). This changes her balance from -\)180 to: \[ -180 + 75 = -105 \]
So now the account balance is -\(105.

4. **Subtract Second Check**: Finally, subtract the amount of the second check (\)90) from the current balance (-\(105): \[ -105 - 90 = -195 \]
This results in the final balance being -\)195.

Therefore, by carefully following each step and performing the correct arithmetic operations, you will accurately determine the final account balance.